Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q2 up to the prior quarter (i.e. 2018 Q1). The test period is a forecast for the current period and includes comparison to the appropriate median rent estimates for data observed so far in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic.

This page was last updated: 2018-06-02




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 309.0099 214.7089 206.7180 199.1160 199.2426
Training 325.0620 141.2202 141.6717 143.6989 142.4653



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 254.0486 154.08054 147.61005 141.22649 141.23755
Training 260.6634 93.81771 93.98435 96.52958 95.68656



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -182.2634 -688.6591 -688.5317 -691.6726 -693.1361



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -181.8581 -670.8105 -670.5209 -673.2715 -674.4199

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 92.9886 7.1199 79.5460 92.8120 107.5357 92.5807
Precision for idtract 30.7903 4.3235 23.0944 30.5172 40.0889 30.0053
Precision for idqtr 3040.2407 3357.8052 391.0750 2039.0533 11798.0230 987.1305
Rho for idqtr 0.2993 0.3652 -0.4779 0.3396 0.8684 0.5134
Precision for idqtr1 17174.5569 21584.3782 458.7981 10027.7571 74828.5879 826.6610



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 92.1729 7.1085 78.8723 91.9412 106.8530 91.5351
Precision for idtract (iid component) 93.2485 24.3536 54.2010 90.3089 149.4276 84.7452
Precision for idtract (spatial component) 86.8944 28.3955 44.5750 82.4383 154.7433 74.2752
Precision for idqtr 3066.6604 3283.5254 409.7747 2090.9074 11596.8835 1035.1454
Rho for idqtr 0.3198 0.3600 -0.4492 0.3595 0.8777 0.5379
Precision for idqtr1 15463.3302 19420.7806 355.7433 8908.2603 67697.5410 562.6353



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 92.6550 7.1855 79.1814 92.4330 107.4635 92.0634
Precision for idtract (iid component) 93.4694 24.4591 54.1573 90.5544 149.8052 85.0360
Precision for idtract (spatial component) 86.6936 28.3669 44.5603 82.1730 154.4628 73.9155
Precision for idqtr 3088.4806 3314.2901 411.2708 2103.3271 11709.6617 1039.1497
Rho for idqtr 0.3151 0.3606 -0.4517 0.3534 0.8764 0.5287
Precision for idqtr1 15415.5212 19372.6604 349.7537 8868.6034 67493.5056 547.0469
Precision for idtractqtr 18437.6937 18247.6988 1271.6058 13052.9674 66741.1035 3480.2117

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)